# Homogenization for a Class of Generalized Langevin Equations with an Application to Thermophoresis

## TL;DR

This paper derives a homogenized model for generalized Langevin equations with state-dependent coefficients, revealing additional drift effects, and applies it to analyze thermophoresis in non-equilibrium heat baths.

## Contribution

It extends existing homogenization results to a broader class of Langevin equations with weaker spectral assumptions and applies the theory to thermophoresis phenomena.

## Key findings

- Homogenized process includes noise-induced drift terms.
- Convergence proven under weaker spectral assumptions.
- Application to thermophoresis in non-equilibrium heat baths.

## Abstract

We study a class of systems whose dynamics are described by generalized Langevin equations with state-dependent coefficients. We find that in the limit, in which all the characteristic time scales vanish at the same rate, the position variable of the system converges to a homogenized process, described by an equation containing additional drift terms induced by the noise. The convergence results are obtained using the main result in \cite{hottovy2015smoluchowski}, whose version is proven here under a weaker spectral assumption on the damping matrix. We apply our results to study thermophoresis of a Brownian particle in a non-equilibrium heat bath.